Consumer Theory

Question 1

What is a commodity space?

Answer 1

A subset of the Euclidean space (real numbers)

Question 2

Define weak preference relation

Answer 2

If the consumer thinks bundle x is as least as good as bundle x’ , we write this as xRx’

Question 3

Define strict preference relation

Answer 3

If xRx’ and not x’Rx , then the consumer thinks x is better than x’ . We write this as
xPx’

Question 4

Define indifference relation

Answer 4

If xRx’ and x’Rx , then the consumer thinks x and x’ are equally good. We write this as
xIx’

Question 5

What are the 3 assumptions of R

Answer 5

R is reflexive, i.e. xRx .
R is transitive, i.e. if xRy and yRx’ , then xRx’ .
R is connected/complete i.e. xRx’ or x’Rx

Question 6

What are the 4 other possible restrictions on preferences?

Answer 6

Convexity
Continuity
Monotonocity
Non-satiation

Question 7

Define convexity

Answer 7

Suppose xIx’ . Then convexity implies yPx’ and yPx

Question 8

Define continuity

Answer 8

Suppose all bundles in A are preferred to all bundles in B. As we move from B to A, continuity implies that there exists a bundle x’ such that xIx’ .

Question 9

Define monotonocity

Answer 9

if x > x’ , then xPx’ (i.e. more is better than less)

Question 10

Define non-satiation

Answer 10

for every bundle x, there always exists some other bundle x’ such that x’Px

Question 11

What is the slope of an indifference curve called?

Answer 11

marginal rate of substitution (MRS)

Question 12

Define an indifference curve

Answer 12

A curve on a graph (the axes of which represent quantities of two commodities) linking those combinations (bundles) of quantities which the consumer regards as of equal value.

Question 13

Describe the indifference curves for perfect substitutes

Answer 13

linear - straight lines

Question 14

Describe the indifference curves for perfect complements

Answer 14

L shaped

Question 15

Can lexicographic preferences be represented by a utility function?

Answer 15

No, because they are not continuous

Question 16

What is MRS equal to?

Answer 16

(dU/dx1) / (dU/dx2)

i.e. Marginal utility wrt x1 divided by marginal utility wrt x2

Question 17

What is a consumer’s budget set

Answer 17

The set of affordable consumption bundles

Question 18

What is the slope of the budget line is equal to?

Answer 18

• p1/p2

Question 19

What are the Marshallian demand functions for perfect complements?

Answer 19

x1 = x2 = m/(p1+p2)

Question 20

What are the Marshallian demand functions for Cobb Douglas?

Answer 20

x1 = am/p1
x2 = (1-a)m/p2

Question 21

What is Roy’s Identity

Answer 21

Given indirect utility function, Roy’s identity can be used to derive the Marshallian demand functions

x1(p1,p2,m) = - (dV/dp1) / (dV/dm)
x2(p1,p2,m) = - (dV/dp2) / (dV/dm)

Question 22

What is Shephard’s Lemma

Answer 22

Given the expenditure function, the Hicksian demand functions can be derived using Shephard’s lemma

h1(p1,p2,m) = dE/dp1
h2(p1,p2,m) = dE/dp2

Question 23

How are the Indirect Utility Function and the Expenditure Function related?

Answer 23

The indirect utility function and the expenditure function are inverses of one another

Question 24

What is the Slutsky equation?

Answer 24

A change in demand with respect to a change in price can be decomposed into a substitution effect and an income effect. This decomposition is given by the Slutsky equation:

dx1/dp1 = dh1/dp1 - (dx1/dm)x1

Question 25

What is the Slutsky equation in elasticity form?

Answer 25

Em = Eh - EiS

Em = Marshallian PED
Eh = Hicksian PED
Ei = Income ED
S = Share of income spent on x

Question 26

What is the Giffen’s Paradox

Answer 26

According to the Law of Demand, when the price of a commodity falls the demand for it rises. Giffen’s Paradox is an exception to this law.
A Giffen good is a special case of an “inferior good” of which people buy less when their income rises e.g. rental housing
In economic terms the income effect dominates the substitution effect.

Question 27

Why might higher wages lead to higher wages can lead to a decline in labour supply?

Answer 27

Backward-Bending Labour Supply Curve

The substitution effect - higher wage makes work more attractive than leisure, supply increases because work gives greater remuneration

The income effect - higher wage means workers can achieve a target income by working fewer hours. Therefore, if wages increase, it becomes easier to get enough income through working fewer hours